Before you run the sample, have a drawing document open that contains several drawing dimensions including unattached (sick) ones.
Public Sub DeleteUnattachedDimensions()
' Set a reference to the active drawing document
Dim oDoc As DrawingDocument
Set oDoc = ThisApplication.ActiveDocument
' Set a reference to the active sheet
Dim oSheet As Sheet
Set oSheet = oDoc.ActiveSheet
Dim oDrawingDim As DrawingDimension
' Iterate over all dimensions in the drawing
' and delete unattached (sick) dimensions.
For Each oDrawingDim In oSheet.DrawingDimensions
If oDrawingDim.Attached = False Then
Call oDrawingDim.Delete
End If
Next
End Sub